Question

Find the length$\mathit{s}$of the arc that subtends a central angle of measure in a circle of radius 12 m.

Short answer

The length of the arc is8.4 m.

Step-by-step solution

Step 1. Given information

The given radius of $\text{circle}=12\text{m}$and the central angle in radian$\theta$ is${40}^{\circ }$

Step 2. Explanation

We will use the formula of arc length,

$s=r\theta$

Step 3. Calculation

First convert the central angle in radian

$\begin{array}{l}\theta =40.\frac{\pi }{180}\\ =\frac{2\pi }{9}\text{\hspace{0.17em}radian}\end{array}$

$\begin{array}{l}\text{Thelengthof\hspace{0.17em}the\hspace{0.17em}arc\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}s=r\theta \\ s=12x\frac{2\pi }{9}\\ s=\frac{8\pi }{3}\\ s=8.4m\end{array}$